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Math  /  Geometry

QuestionThe right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer Attempt 2 out of 2

Studdy Solution

STEP 1

What is this asking? We need to figure out how much bigger one triangle is than the other. Watch out! Make sure to simplify the fraction at the end!

STEP 2

1. Set up the scale factor equation
2. Solve for the scale factor

STEP 3

Alright, so we've got two right triangles, one big and one small, and we know they're scaled copies of each other.
That means their corresponding sides are proportional.
Let's call the **scale factor** kk.

STEP 4

We can **set up a proportion** relating the corresponding sides.
Let's use the sides labeled 1313 and 133\frac{13}{3}.
We can say that the **scale factor** kk times the **original side length** 1313 equals the **new side length** 133\frac{13}{3}.
So, we have: k⋅13=133k \cdot 13 = \frac{13}{3}

STEP 5

Now, we want to **isolate** kk.
To do this, we can **divide both sides** of the equation by 1313.
Remember, dividing by 1313 is the same as multiplying by 113\frac{1}{13}.
So, we're really multiplying both sides by 113\frac{1}{13} to turn that 1313 on the left side into a 11. 113⋅k⋅13=113⋅133 \frac{1}{13} \cdot k \cdot 13 = \frac{1}{13} \cdot \frac{13}{3}

STEP 6

On the left side, we have 113⋅13\frac{1}{13} \cdot 13, which equals 11.
On the right side, we have 113⋅133\frac{1}{13} \cdot \frac{13}{3}, which equals 1313⋅3\frac{13}{13 \cdot 3}.
Since 1313\frac{13}{13} is just 11, the right side simplifies to 13\frac{1}{3}.
So, our equation becomes: k=13 k = \frac{1}{3}

STEP 7

The scale factor is 13\frac{1}{3}.

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